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Position-encoded microsphere arrays are a promising technology for identifying biological targets and quantifying their concentrations. In this paper we analyze the statistical performance of these arrays in imaging targets at typical low signal-to-noise ratio (SNR) levels. We compute the Ziv-Zakai bound (ZZB) on the errors in estimating the unknown parameters, including the target concentrations. We find the SNR level below which the ZZB provides a more accurate prediction of the error than the posterior Cramér-Rao bound (PCRB), through numerical examples. We further apply the ZZB to select the optimal design parameters of the microsphere array device and investigate the effects of the experimental variables such as microscope point-spread function. An imaging experiment on microspheres with protein targets verifies the optimal design parameters using the ZZB.